A007575 Number of stable towers of 2 X 2 LEGO blocks. (Formerly M2675)

1, 3, 7, 19, 53, 149, 419, 1191, 3403, 9755, 28077, 81097, 234861, 681697, 1982723, 5777375, 16861521, 49281525, 144222987, 422566835, 1239423303, 3638872529, 10693065215, 31448140529, 92558787745, 272612601065, 803448576111

Offset

0,2

References

Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 65.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

P. J. S. Watson, On "LEGO" towers, J. Rec. Math., 12 (No. 1, 1979-1980), 24-27.

Links

Ray Chandler, Table of n, a(n) for n = 0..2098 (terms < 10^1000)

Andrei Asinowski, Axel Bacher, Cyril Banderier, Bernhard Gittenberger, Analytic combinatorics of lattice paths with forbidden patterns, the vectorial kernel method, and generating functions for pushdown automata, Laboratoire d'Informatique de Paris Nord (LIPN 2019).

P. J. S. Watson, On "LEGO" towers, J. Rec. Math., 12 (No. 1, 1979-1980), 24-27. (Annotated scanned copy)

Index entry for sequences related to LEGO blocks

Formula

a(n) ~ 3^(n+1) / sqrt(Pi*n). - Vaclav Kotesovec, Jul 11 2018

Maple

seq(sum(coeff(product(1+x^k+x^(2*k), k=1..n), x, l), l=n*(n+1)/2-n..n*(n+1)/2+n), n=0..20); # Søren Eilers

Mathematica

Array[Sum[SeriesCoefficient[Product[1 + x^k + x^(2 k), {k, #}], {x, 0, j}], {j, # (# + 1)/2 - #, # (# + 1)/2 + #}] &, 27, 0] (* Michael De Vlieger, Feb 24 2020, after Maple *)

Crossrefs

Cf. A007576.

Sequence in context: A007180 A090378 A059506 * A026299 A183117 A183124

Adjacent sequences: A007572 A007573 A007574 * A007576 A007577 A007578

Keyword

nonn

Author

Simon Plouffe and N. J. A. Sloane, Robert G. Wilson v

Status

approved